Kernel refers to weighting functions used in non-parametric estimation techniques.
0
votes
0answers
18 views
Difference between Kernel classifier and linear classifier
I would just like to know what are the differences between kernel classifier and linear classifier?
In what kind of problems the first is used and in what kind the second?
What could be the ...
0
votes
0answers
30 views
What is the minimum number of data points required for kernel density estimation?
What is the minimum number of data points required for a kernel density estimation to be considered non-misleading/acceptable/adequate?
Is there a some rule based on how dispersed the data is?
For ...
0
votes
1answer
52 views
Applying kernel function to input data before giving it to algorithm
I have gene expression data, I do dimensionality reduction and clustering with self organizing maps, but self organizing maps do not perform well with my data.
I want to map my data to feature space ...
3
votes
1answer
80 views
What are the limitations of Kernel methods and when to use kernel methods?
Kernel methods are very effective in many supervised classification tasks. So what are the limitations of kernel methods and when to use kernel methods? Especially in the large scale data era, what ...
4
votes
1answer
104 views
“Kernel density estimation” is a convolution of what?
I am trying to get a better understanding of kernel density estimation.
Using the definition from Wikipedia: https://en.wikipedia.org/wiki/Kernel_density_estimation#Definition
$
\hat{f_h}(x) = ...
2
votes
1answer
38 views
From half-circle to linear model
this is kinda homeworkish so I don't want a full solution I just want some input.
I have this data set
And I want to transform the data (with a rbf Kernel?) in order to be able to do a simple ...
6
votes
2answers
181 views
Linear kernel and non-linear kernel for support vector machine?
When using support vector machine, are there any guidelines on choosing linear kernel vs. nonlinear kernel, like RBF? I once heard that non-linear kernel tends not to perform well once the number of ...
0
votes
0answers
24 views
Kernel/Basis function design with regularizer
I am solving this problem:
$$
\sum_i \parallel f(x_i)- y_i\parallel_2^2 + \lambda <\psi f, \psi f>_{L_2}^2
$$
where the second part $<\psi f, \psi f>_2^2$ is regularizer using the linear ...
2
votes
1answer
63 views
Relationship between the kernel and the value of C in SVM's
How exactly does the value of C relate across different kernels that we can use for SVM's? As in, how does it vary when changing the polynomial degree of a kernel or while using a Gaussian kernel?
1
vote
0answers
40 views
strange density plot of p-value [duplicate]
I computed the T-score and P-value using t.test() for my data, and finally I've plotted the density of my p-value and I've got strange plot. I don't know, why I see ...
2
votes
1answer
61 views
Kernel density estimation - application
What is the validity of using a kernel-density-estimation to compare model x observed data?
In other words, if the KDE curve for the observed data looks like the KDE for the model forecast, can I use ...
0
votes
0answers
48 views
Where does the square root for a polynomial kernel mapping function come from?
I'm trying to understand how polynomial kernel functions work, in my textbook it shows an example with a degree of 2, with an input dimension of 2:
$K(\vec{x}, \vec{y})$ = $(1 + x_1y_1 + x_2y_2)^2$
...
0
votes
0answers
42 views
Kernel density estimation for a variable with lots of zeros [duplicate]
I am trying to estimate the kernel density for number of days a child is sick. Around 73% of children report not being sick, i.e. zero. How do I estimate a kernel density for this censored variable ...
1
vote
0answers
24 views
SVM kernel mapping, finding boundaries in projected space
I have a question about the support vector machine (SVM) kernel trick. How do you find the boundaries of the training data set in kernel projected space? Is that the same boundaries as you can obtain ...
0
votes
0answers
21 views
Value for Kernel Density Estimation is > 1 [duplicate]
I have 80 2D data points (located here) and am trying to estimate the pdf at a point $x$ by using a multivariate kernel density estimate.
The mean vector is $\mu = [0.0368418, 0.0157501]$ and ...
1
vote
0answers
19 views
Local Kernel for Rate Data
Perhaps a naive question here. Is there a local kernel-based approach that is appropriate for modeling rate data of the form y/z, in which y can be 0 but z never is? Omitting z and measuring the mean ...
0
votes
0answers
106 views
I am still confused with Gaussian kernel in SVM
From the slides http://www.csie.ntu.edu.tw/~cjlin/talks/kuleuven_svm.pdf,
$$\min \frac{1}{2}w^Tw $$
subject to $$y_i(w^T\phi(x_i)+b)\ge 1,i=1,\cdots,n$$
I think most people are very familiar with ...
7
votes
2answers
234 views
The Gaussian kernel
In SVM, the Gaussian kernel is defined as:
$$K(x,y)=\exp\left({-\frac{\|x-y\|_2^2}{2\sigma^2}}\right)=\phi(x)^T\phi(y)$$ where $x, y\in \mathbb{R^n}$.
I do not know the explicit equation of $\phi$. I ...
5
votes
4answers
161 views
Smooth a circular/periodic time series
I have data for motor vehicle crashes by hour of the day. As you would expect, they are high in the middle of the day and peak at rush-hour. ggplot2's default geom_density smooths it out nicely
A ...
2
votes
0answers
25 views
Kernel regression with monotonicity constraints
I need to fit a bivariate data using kernel regression (local polynomial regression).
It should satisfies two conditions.
$\frac{dy}{dx_1} \geq 0$ for all $x_2$
$\frac{dy}{dx_2} \geq 0$ for all ...
1
vote
0answers
43 views
How to calculate confidence intervals using subsampling after a nonparametric estimator about the empirical distribution function?
I have a problem where I think subsampling is more appropriate than the bootstrap. (Reason in another post.)
However, I found no quick reference on subsampling CIs, and my naive inversion of the ...
2
votes
0answers
43 views
Is excess mass estimation smooth enough to bootstrap? At what rate might a bunching estimator converge?
The recent public finance literature often estimates relative excess mass around specific points of the earnings distribution ("kink points" or "notches" of tax schedules, say), and then bootstraps to ...
0
votes
1answer
92 views
Trouble with kernel in kernlab R package
I'm using kernlab package
Here are two examples:
First:
...
14
votes
4answers
435 views
Good methods for density plots of non-negative variables in R?
plot(density(rexp(100))
Obviously all density to the left of zero represents bias.
I'm looking to summarize some data for non-statisticians, and I want to avoid ...
0
votes
0answers
32 views
Choice of sigma in Gaussian kernel for dimensionality reduction? (small sample size)
I am working on dimensionality reduction concerning large simulation data. So unusual for Machine Learning, the sample size is a lot smaller ($\approx 150$) than the dimension of the data ($\approx ...
3
votes
2answers
139 views
Implementing kernel logistic regression using IRWLS
I am referring to [1] for implementing Kernel Logistic Regression using IRWLS.
In logistic regression, the form of the regularized negative log-likelihood we aim to minimize is the following:
$$L(w) ...
1
vote
0answers
90 views
Generalized RBF Kernels
There is the notion of Generalized RBF Kernels, for example in
"Towards Optimal Bag-of-Features for Object Categorization and Semantic Video Retrieval" from Jiang (1) or in formula (2.72) in ...
0
votes
1answer
274 views
Use Gaussian RBF kernel for mapping of 2D data to 3D
I am working on SVMs and try to get all the concepts involved. For instance, the kernel mapping. I would like to construct some parts of the algorithm by myself, to understand what is happening.
My ...
0
votes
0answers
51 views
What are some fast graph kernel methods?
I am doing a project on network community detection via “Kernel Spectral Clustering” where the most commonly used kernel is RBF kernel. My project is to apply ...
5
votes
2answers
216 views
Integrating kernel density estimator in 2D
I'm coming from this question in case anybody wants to follow the trail.
Basically I have a data set $\Omega$ composed of $N$ objects where each object has a given number of measured values attached ...
0
votes
1answer
141 views
Gaussian Kernel function vs normal distribution function
I read from this link and thought that kernel density functions are used for solving the unrealistic normal distributions or specification errors. But when I read the description of kernel density in ...
1
vote
1answer
117 views
Prove (or disprove) that this function is a kernel
I devised a distance function similar to this form
$d(x,y) = \sum_{i = 1}^{n-1} b(x_i, y_i,x_{i+1}, y_{i+1}) $
with
$b(x_i, y_i,x_{i+1}, y_{i+1}) = 0 \mbox{ if } x_i \leq 0 \vee y_i \leq 0 \vee ...
0
votes
0answers
195 views
Kernel density estimation (CDF) with Epanechnikov kernel in Matlab
The code for Kernel density estimation was given in a recent CrossValidated question by Julio Miguel Galvez entitled "Kernel density estimation with Epanechnikov kernel in Matlab", as follows.
How ...
2
votes
1answer
64 views
Understanding the mean shift algorithm with Gaussian kernel
I am referring here to the Wikipedia article regarding the mean shift algorithm.
Here the Gaussian kernel is denoted as $e^{-c\|x_i - x\|^2 }$
My questions are the following:
Is $c$ always ...
3
votes
1answer
149 views
Difference between a SVM and a perceptron
I am a bit confused with the difference between an SVM and a perceptron. Let me try to summarize my understanding here, and please feel free to correct where I am wrong and fill in what I have missed. ...
0
votes
0answers
45 views
Modeling multivariate density with semiparametric methods
I am trying to model (using R) the density of multivariate data conditioned on a few known parameters so I can simulate sampling from new sets of parameters.
I have about 100,000 data points that ...
3
votes
2answers
119 views
Loss for Kernel Ridge Regression
Is $||Y-X\beta||_2^2 + \lambda\beta^T K\beta$ , the standard loss-function in kernel ridge regression, or is it different? Also, is the gaussian kernel a standard choice used for the kernel, in ...
1
vote
1answer
48 views
Mode estimation in high dimensions
Suppose we have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$-dimensional unimodal density $f(\boldsymbol{x})$. I would like to estimate the mode of $f(\boldsymbol{x})$.
The ...
2
votes
0answers
46 views
Fast multivariate unimodal density estimator
I have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$ dimensional density $f(\boldsymbol{x})$ and I would like to estimate this unknown density. In addition I know that ...
0
votes
2answers
93 views
Kernel density estimation (KDE)
Due to an assignment I need to implement a algorithm based on KDE to schedule an input data in different servers.
So far, I studied statistics in my bachelor but we did not go that far and they did ...
4
votes
2answers
157 views
Kernel density estimator that doesn't collapse in the tails
I have iid data-points $x_1, \dots, x_n$, generated by an unknown density $f(x)$.
So far I have approximated $f(x)$ with a normal $N(\hat{\mu}, \hat{\sigma}^2 )$, where $\hat{\mu}$ and ...
1
vote
1answer
214 views
How to understand effect of RBF SVM
How can I understand what the RBF Kernel in SVM does? I mean I understand the maths, but is there a way to get a feeling when this kernel will be useful?
Would results from kNN be related to SVM/RBF ...
0
votes
1answer
90 views
The Lagrange multipliers of SVM
Actually the solve the SVM is to solve the following Lagrangian Equation:
If we don't use kernel function, $\langle x^{(i)},x^{(j)}\rangle$ is just the vector vector inner product. The ...
0
votes
0answers
37 views
Smoothing of log-distributed periodogram
I use the lomb-scargle periodogram to output information about chemical species in distinct time periods. This produces a distribution that is skewed heavily, with the majority of points and variance ...
2
votes
3answers
129 views
How to explain how I divided a bimodal distribution based on kernel density estimation
I have a dataset of bimodal population. It contains a smaller peak, which is considered to be "bad", and a bigger peak. I try to separate the bad part of data from the rest of data. What I did was: ...
1
vote
1answer
87 views
Evaluating features and similarity measures
I am currently developing a classificator, which is supposed to classify into a number of classes. For this purpose I am
designing some features and similarity measures which I might use for a later ...
4
votes
2answers
91 views
Why are these proper kernels and how to deduce that they are?
I am struggling to understand kernels and how to determine whether they are proper or not.
For these examples can anyone explain why an example is proper and why another example is not.
Given K1 and ...
0
votes
1answer
103 views
Is it legitimate to use a conditional PDF derived using kernel density estimation for hypothesis testing?
Suppose I have some sample $X$ drawn from some unknown multivariate distribution $F(A,B)$, and I want to test the null hypothesis that a particular point $x$ was drawn from $F$.
Would it be ...
0
votes
1answer
394 views
how to read y axis in kernel density graph [duplicate]
I need to understand how to read kernel density graphs. How do you come up with the values in y-axis?
1
vote
1answer
155 views
Number of kernel evaluations in SVM training
What is the typical number of kernel evaluations (between two training vectors) performed during a (kernelized) Support Vector Machine (SVM) training?
I am asking this question because I need to ...
